Geodesic
Generalized Bessel Function Associated with Dihedral Groups
Journal of Lie theory, Tome 22 (2012) no. 1, pp. 81-91

Voir la notice de l'article provenant de la source Heldermann Verlag

Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas for Fourier and Radon transforms to derive a closed formula for this series when the parameter of the Gegenbauer polynomial is a positive integer. As a by-product, we get a relatively simple integral representation for the generalized Bessel function associated with dihedral groups Dn, n ≥ 2 when both multiplicities sum to an integer. In particular, we recover a previous result obtained for D4 and we give a special interest to D6. Finally, we derive similar results for odd dihedral groups.
Classification : 33C52, 33C45, 42C10, 43A85, 43A90
Mots-clés : Generalized Bessel function, dihedral groups, Jacobi polynomials, Radon Transform 
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     author = {N. Demni },
     title = {Generalized {Bessel} {Function} {Associated} with {Dihedral} {Groups}},
     journal = {Journal of Lie theory},
     pages = {81--91},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_1_JLT_2012_22_1_a2/}
}
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N. Demni . Generalized Bessel Function Associated with Dihedral Groups. Journal of Lie theory, Tome 22 (2012) no. 1, pp. 81-91. http://geodesic.mathdoc.fr/item/JLT_2012_22_1_JLT_2012_22_1_a2/